What is superelevation?

Superelevation (e) is the banking of a roadway along a horizontal curve achieved by raising the outer edge above the inner edge. By tilting the pavement cross-section inward, a component of vehicle weight acts toward the center of the curve, supplementing tire friction and allowing higher safe speeds.

What is the AASHTO superelevation formula?

AASHTO uses e + f = V²/(127·R) in SI units (V in km/h, R in m) or e + f = V²/(15·R) in US customary (V in mph, R in ft). Here e is the superelevation rate (decimal) and f is the side friction factor.

What is a typical maximum superelevation rate?

AASHTO recommends e_max of 0.04 (4%) for urban areas with frequent access, 0.06 for rural highways, and up to 0.08–0.12 for high-speed rural highways and areas without snow/ice. The input defaults to 0.08.

How is the side friction factor f chosen?

AASHTO provides f values by design speed: roughly 0.18–0.40 at 20 km/h down to 0.10–0.14 at 130 km/h. Higher speeds require lower f assumptions because driver comfort limits lateral force perception, not just tire capability.

What does a negative required e mean?

If the calculated e is negative, the curve radius is large enough that normal friction alone (or even a negative cross-slope/adverse crown) handles the speed. No positive superelevation is needed; the road can remain normally crowned.

How is minimum curve radius derived?

R_min = V²/[127·(e_max + f_max)] in SI. This is the tightest radius at which a vehicle can travel at design speed given the maximum allowable superelevation and friction.

Curve Superelevation Calculator

Enter design speed, curve radius, and friction coefficient to get the required superelevation rate, banking angle, and minimum safe radius for a horizontal road curve.

Curve Parameters

Units:

Design Speed (km/h)

Typical range: 30–130 km/h (20–80 mph).

Horizontal Curve Radius (m)

Enter the radius to the road centerline.

Max Side Friction Factor f

AASHTO: ~0.14 at 80 km/h (50 mph); ~0.17 at 60 km/h (40 mph).

Max Superelevation e_max (decimal)

0.08 = 8%. AASHTO max: 0.04–0.12 by context.

Required e

—

Banking Angle

—

degrees

Design Parameters & Results

Design speed —

Curve radius —

Side friction factor f —

Centrifugal force ratio e + f —

Required superelevation e —

Banking angle θ —

Minimum safe radius (at e_max, f) —

Margin to minimum radius —

Road Cross-Section (schematic)

Banking exaggerated for clarity. Center of curve is to the left.

Formula Reference (AASHTO)

SI formula e + f = V² / (127 · R)

US customary formula e + f = V² / (15 · R)

Banking angle θ = arctan(e)

Min. radius R_min = V² / [K · (e_max + f)]

Enter curve parameters and click Calculate Superelevation.

Required banking angle and AASHTO design checks will appear here.

Summary

Superelevation (e) is the transverse slope applied to a roadway on a horizontal curve so that vehicles can navigate at design speed without relying entirely on tire friction. This calculator applies the AASHTO formula e + f = V² / (127 · R) (SI) or e + f = V² / (15 · R) (US customary), where V is design speed, R is curve radius, and f is the maximum side friction factor. Results include the required superelevation rate, banking angle in degrees, minimum curve radius for the entered e and f limits, and the centrifugal force ratio.

How it works

Enter the design speed (km/h or mph) and select the unit system.
Enter the horizontal curve radius in meters or feet.
Enter the maximum side friction factor f (AASHTO tables by design speed).
Enter the maximum superelevation rate e_max (typically 0.04–0.12 as a decimal).
The calculator solves e = V²/(127·R) − f for SI, or e = V²/(15·R) − f for US customary.
Results show required e, banking angle, minimum radius, and centrifugal force ratio.

Use cases

Checking AASHTO superelevation requirements for a new highway alignment.
Verifying existing road banking adequacy for a posted speed limit.
Computing minimum horizontal curve radius during preliminary design.
Transportation engineering coursework and PE exam preparation.
Evaluating safety of low-speed curves on secondary roads.
Comparing metric and US customary superelevation calculations.

Frequently Asked Questions

Last updated: 2026-06-15 · Reviewed by Nham Vu